SPATIAL PREDICTIVE MAPPING USING ARTIFICIAL NEURAL NETWORKS

The modelling or prediction of complex geospatial phenomena (like formation of geo-hazards) is one of the most important tasks for geoscientists. But in practice it faces various difficulties, caused mainly by the complexity of relationships between the phenomena itself and the controlling parameters, as well by limitations of our knowledge about the nature of physical/ mathematical relationships and by restrictions regarding accuracy and availability of data. In this situation methods of artificial intelligence, like artificial neural networks (ANN) offer a meaningful alternative modelling approach compared to the exact mathematical modelling. In the past, the application of ANN technologies in geosciences was primarily limited due to difficulties to integrate it into geo-data processing algorithms. In consideration of this background, the software advangeo® was developed to provide a normal GIS user with a powerful tool to use ANNs for prediction mapping and data preparation within his standard ESRI ArcGIS environment. In many case studies, such as land use planning, geo-hazards analysis and prevention, mineral potential mapping, agriculture & forestry advangeo® has shown its capabilities and strengths. The approach is able to add considerable value to existing data.


INTRODUCTION
The identification of potential risk areas for humans, animals, real estate, infrastructure or the localization of potential mineral resources are essential for both society and economy.Specific questions as "Where is a high geohazard risk and which preventive measures are possible?","Where are mineral exploration targets" or "What are reasonable measures to avoid a pest infestation?"should be answered efficiently and in acceptable time.
A growing amount of available geo-scientific data and the ongoing improvement of information technology are an excellent base for a broad data analysis aiming at getting more information about crucial relationships and interconnections as a fundament of the creation of predictive maps.
Generally, spatial phenomena/events can be modelled by various approaches, including:  mathematical-analytical methods for an accurate modelling of the processes conducting detailed studies of physical, chemical and other dependencies,  by an empirical or statistical approach, evaluating potentially factors with multivariate methods, based on data analysis and expert experiences and  geo-statistical modelling of the event.
The mathematical-analytical approach is a time and cost consuming process, which requires much model calibration.In most cases the approach is not really applicable because of data and knowledge limitations.
Geo-statistical approaches like "Kriging" interpret the spatial distribution and correlation of parameters, but do not consider other influencing factors that are relevant for the appearance of the quested event.This method is often used for regionalization of parameters, e.g.like soil contamination, or mineral deposit grade models.
Multivariate approaches (Backhaus et al., 2003) which are considering different influencing factors and their relationships and allowing a certain generalization play an important role in data modelling.Modern computer science is able to calculate complex models using a large set of influencing factors and a big number of datasets.
Compared to the exact mathematical-analytical modelling, multivariate approaches offer several advantages:  they are applicable even if the relationships between the depending variable and the influencing factors are not really known. they consider many influencing factors  they work with available data  they are comparable quick and easy to use.

METHOD: ARTIFICIAL NEURAL NETWORKS
Artificial neural networks (ANN) allow a multivariate data analysis of complex problems.Their ability to learn from given examples without an explicit programming of problem solution allows a ubiquitous application.Even if the user does not really understand details of the relationships between the depending value and the controlling factors, the generation of a "footprint" by using given examples is possible.Another important advantage of ANN is its ability to generalize: unknown but similar input patterns of input data could also produce a plausible result.
Various authors have successfully applied ANN to forecast the occurrence and extent of spatial events.Examples of applications have included the accurate identification of slope failure processes (Fernandez-Steeger 2002), the modelling of spatial air pollution patterns (Lin et al. 2004) or the propagation of flood waves (Peters et al. 2006).Beak Consultants GmbH uses artificial neural networks for the modelling of geoscientific problems since 2006.
The ANN approach is based on the functionality of a biological nervous system.This system is composed of many interconnected neurons (nerve cells), which receive process and transfer information.After reaching a certain threshold, nerve cells are activated and forward the information to other connected neurons.During a learning process the interconnections are adapted.The simulation of these biochemical processes in an ANN is realized by artificial neurons.The connections are realized by directed interconnection weights (Backhaus et al. (2003) and Kriesel (2009)).
Artificial neural networks are usually organized in layers.The network topology describes the number of layers, the number of neurons in layers and the way of their interconnection: Important parameters are the direction of signal propagation (forward / backward) and the type and level of connection (completely connected / with shortcuts).Figure 1 shows a completely connected feed-forward network with 4-3-1 topology.On the right-hand side, a processing unit (neuron) is sketched with its input, output and activation functions.During the learning process the weights are adapted: After each iteration of processing the input information to output, the mean squared error (MSE) is calculated between expected and actual outputs (between modelled and real training data).The weights were adapted by using a defined learning algorithm with the aim of error minimization.The training is stopped after reaching a defined count of iterations (epochs) or if the error falls below a defined minimum.Typical learning algorithms are the "Backpropagation of Error" (BackPROP) or derivatives like the "Resilient Backpropagation" (RPROP).
The strength of the interconnections in the calibrated model depends on the influence of the potential factor or a set of factors and their relationships.

INTEGRATION OF THE METHOD INTO GIS: SOFTWARE ADVANGEO ®
Originally, ANNs where used for data analysis of medical applications or for solving different mathematical problems.Typical input data have a manageable amount of datasets describing the problem.
In spatial data analysis, the amount of data records which has to be analysed, is often very high.Depending on the data resolution this could easily be more than a million records.
Until now, the effort to prepare the amount of geo-data for using the ANN approach and the absence of interfaces to existing class libraries and tools, causes the rarely use of ANN for the modelling of geo-scientific problems in GIS.
The software advangeo® was implemented using the GIS software ArcGIS from ESRI®.Advangeo® enables the GIS user processing their spatial data within their common GIS environment.
The modelling core of the software is based on an artificial neural network which uses the Multilayer perceptron (MLP).
The MLP is trained in a supervised learning process.Training data (known event locations) are used to derive the relationships between the depending variable (the event/ phenomena) and the controlling parameters.
The depending variable can be nominal for a qualitative modelling.But it can also have a higher scale level for a quantitative modelling.In this case the training data set must be appropriately scaled.

Graphical User Interfaces and Functionality
For its data processing, advangeo uses the functionality of ESRI ArcGIS.Since the modelling approach is a raster analysis, the "Spatial Analyst" extension is required.
Main user components of the application are the standalone Data-and Model Explorer and a GIS-Extension (see Figure 2).The Data-and Model Explorer allow the creation and administration of projects including the organization and processing of geo-data and the parameterization and calculation of the models.In the graphical user interface, the project and its data are organized in a Windows like tree structure.The GIS extension is communicating with the Data-and Model Explorer and supports the data exchange between the user interfaces.It consists of a toolbar and a project tree view.
The project, the logged working steps and all models including the whole metadata are store in a database.The storage of the database itself as well as of the physical data is carried out in a closed file structure: this allows the simple copy and paste of projects from user to user or to another storage medium.An overview of the architecture of advangeo® is shown in Figure 3.

Workflow
Advangeo® consists of different modules, offering an integrated workflow that guides the user through the different work steps of data pre-processing and model creation: The modelling and result presentation is based on raster data (ESRI Grid).For the import to "Source Data" and "Processed Source Data" raster and vector data can be used.
The data processing of the Source Data to create the Processed Source Data can be executed manually using ArcGIS.As an alternative the advangeo® extensions for "Minerals" and "Erosion" are developed for the automation of the processing steps from Source data to ready to use Model Input Data.

Software extensions
Considering the modelling of the data is carried out as a raster analysis, the neighbourhood of a pixel is not interpreted.Therefore, all important information like the distance of a point to a fault or a contaminated site must be derivate from source data information.This data processing requires an extensive knowledge of data manipulation techniques as well as a lot of time.To support the user in complex and often repeated steps of data preparation, two extensions for an automated data processing were implemented:  Erosion Extension: processing of digital elevation models, soil maps and land use maps and the combination of geological data with information of the elevation model (see Figure 4) to prepare data for the modelling of erosion based processes. Minerals Extension: automated processing of geological maps, classification of linear elements and rock contact zones, processing of geophysical data and geochemical data, interpolation of point data to prepare data for the modelling of mineral occurrences based processes.
Both extensions consist of graphical user interfaces for data selection, execution of processing operations.As result ready to use model input data are created.Prediction of mineral potential areas (e.g.Barth et al., 2009), (Barth et al., 2010), (Arkhipova, 2013) and (Nuspl, 2012) and  Prediction of the ground liquefaction risk potential of lignite mining waste dumps (Kallmeier et al., 2014) Below, three examples are described.

Case Study 1: Ground liquefaction risk potential of lignite mining waste piles
In the Lusatian Region, Germany, in former lignite mining areas rising groundwater is causing substantial deformations of the surface in waste rock pile areas.These deformations are caused by ground liquefaction processes and endanger the safety and the post mining use of the respective areas.
Advangeo® was used to create large scale liquefaction hazard potential maps in a test area of the open cast pit "Schlabendorf-Süd".
The following input data were available for modelling:  Considering the permanent changes of the groundwater table, the analysis of the process was focussed to the year of 2010.The model resolution was set for 25 m.By an extensive sensitivity analysis (132 scenarios) the influence of 35 single parameters on the hazard potential were investigated.
To evaluate the influence of a single parameter or a combination of parameters, histograms of the model results can be used: 1.) for the entire area and 2.) for areas with known events.Significant parameters show a clear shift of the maximum to the right side of the histogram for the known events.
As an example for a sensitive parameter the histograms of "thickness of saturated dump" are shown in Figure 6.Finally, the artificial neural network trained with 2010 data was successfully applied to data sets of the years 2008 and 2011.
The respective results show a good match with the events known from these years.The model can be used to predict hazard potential areas in the forthcoming years.

Case Study 2: Gold Potential Mapping in Ghana
The identification of exploration targets is one of the most ambitious tasks in geology.Correct mineral predictive maps safe considerable exploration funds, help to mitigate land use conflicts, reduce environmental damages and can be used for investment attraction The study area of about 60,000 km² is located in Southwest Ghana, West Africa.The model area is famous for greenstone belt related hard rock gold deposits and the derived placers.
The following data sets were available for modelling:  a mineral occurrence database  the geological map 1:1.000.000 airborne magnetic data  the elevation model.
According to the different genetic types of gold deposits different input data layers have been created.The model can easily be upgraded with new exploration data.
As a result of the extensive data analysis and modelling, a gold potential map in a scale of 1: 1,000,000 (see Figure 10) was created.This map provides an excellent base for exploration targeting, investment promotion and small scale mining guidance.The modelling results are shown in the "Placer Gold Potential Map" in a scale 1: 1,000,000 (see Figure 11).The study has proven the general applicability of the approach to analyse and predict forest infections by Ips typographus L. A difficulty was to find an appropriate model which can be used for different epoch characteristics.In future studies more parameters such as information about pre-infection, executed mitigation measures and possibly climate information should be considered.In principle, both qualitative and quantitative analysis of infections was possible with ANN and methods of supervised learning.

CONCLUSIONS
Artificial neural networks are an efficient instrument to model the relationships between a depending variable and the influencing factors of any kind of geo-related problem.
The approach is a consequently data driven, and by this avoids the biased influence of a scientist.The knowledge of the expert is essential for the selection and preparation of input data and for the validation of the results.
Advangeo® provides the software environment for effective data pre-processing, step-by-step model generation, and result visualisation.It is a tool to build up structured and comprehensible models within the widely used ESRI GIS environment.The software will be further developed to improve its usability and functionality.Currently, two other approaches are in the implementation process: Weights of Evidence as an alternative data driven method and Fuzzy Logic for knowledge based data modelling.

Figure 1 .
Figure 1.Scheme of a feed-forward artificial neural network

Figure 2 .
Figure 2. Software advangeo® graphical user interfaces: Data and Modell Explorer (left) and GIS Extension (right)

Figure 4 .
Figure 4. Example of a workflow for processing geological data in the Erosion extension Areas of ground instability (training data)  The recent elevation model  Geometrical data of the former pit  Groundwater table data  Lithological composition of the lignite overburden (exploration data) & Mining technology data For modelling purposes a set of 35 derived independent parameters have been created, such as:  Thickness of the dump(s)  Thickness of the groundwater saturated dump  Thickness of unsaturated dump  Lithological composition of the dump  Hydrogeological data: gradients, flow direction A principle modelling scheme is shown in Figure 5.

Figure 5 .
Figure 5. Scheme of model configuration

Figure 6 .
Figure 6.Histograms of the parameter "Thickness of saturated dump", left: for the entire model area, right: for areas with known events The best fitted model was based on a combination of 15 input parameters: the elevation model and derived data, thickness and composition of the dump and groundwater characteristics.The result of this model is displayed in Figure 7. Observed events are outlined in black.

Figure 7 .
Figure 7. Prediction map based on the known events 2010

For
Figure 8. Pre-processing of tectonic data

Figure 9 .
Figure 9. Evaluation of prospects with regard to their potential High potential prospects can clearly be separated from prospects with less potential.

Figure 12 .
Figure 12.Overview of number of infections per year

Figure 13 .
Figure 13.Prediction map for endangerment of infection by Ips Typographus L. in the National Park "Sächsische Schweiz" in Saxony, Germany Finally, two maps were created by clipping identical models (with identical model input data and net parameters) from different epochs: one for a model considering only the forest stand (percentage of spruce and height, see Figure 13) and one model considering the controlling factors forest stand and location parameters (topographic wetness index, hillshade and density of stand).